In the fabrication of semiconductor components, photolithography is often used for the micropatterning of a semiconductor substrate. The task of the photolithography is to transfer structures from a photomask to a semiconductor substrate. In accordance with a basic concept of photolithography, desired regions of a radiation-sensitive photoresist layer on the semiconductor substrate are irradiated in such a way that only the irradiated or only the unirradiated regions can be removed in a suitable developer. The resulting resist pattern on the semiconductor substrate then serves as a mask for the subsequent process step, such as an etching or an ion implantation, for example. The photoresist layer can subsequently be stripped away again.
In this case, the surface of the semiconductor substrate can be irradiated by means of a demagnifying projection exposure in which the image of the photomask, demagnified by means of a lens system, is projected onto the photoresist surface of the semiconductor. The demagnification generally lies between 1 and 10.
In order to improve the photolithography, use is made of simulations with the aid of which it is possible to assess the optical imaging properties during the production of mask structures that are as small as possible and the mask geometry can be optimized. In this case, an optical proximity correction method, disclosed in the document [1], is often employed. This is understood to be the method by which mask structures are altered geometrically in order to improve the imaging properties. In this case, traditional photolithography simulation assumes a simplified and idealized transmission model for the photomask. This is disclosed in document [1].
Whereas this does not pose a problem in conventional binary masks, in phase masks effects occur which can be described by such a transmission model. In a binary mask, a distinction is made only between light-transmissive and light-opaque regions of the photomask. Phase masks are photomasks provided with regions having a different optical path length which effect a phase shift of the light in adjacent regions with respect to one another. Phase masks are subdivided into halftone phase masks, which are coated with a partially light-transmissive material, in particular with molybdenum-silicon, and alternating phase masks or strong phase masks, on which are provided phase-shifting structures which, in contrast to the halftone phase masks, are completely light-transmissive. Colloquially, phase masks are generally often understood to mean the halftone phase masks. A special case of the alternating phase masks is formed by phase assist masks, in which there are phase-shifting auxiliary structures which, however, in contrast to the alternating phase masks, are fashioned so small that they are not imaged. Hereinafter, we will use the term phase masks for the term phase assist masks.
In order to be able to describe the transmission effects of a mask, it is necessary to precisely describe the three-dimensional mask geometry and the material or materials of which the phase assist is composed, and to solve the resulting Maxwell's equations by complex numerical methods. In these methods, the refraction of a light wave incident on the mask, which is given by its electrical and magnetic field components, is calculated and the resulting field distribution at the mask surface is determined.
Due to the high computational complexity, only masks with simple geometries can be analyzed in this way. This makes it more difficult to develop new photolithography solutions and has hitherto precluded the application of photolithography simulations for the optical proximity correction methods.
The documents [2] and [3] disclose the simulation of masks, mask geometry structures for which deviations from the ideal mask model are to be expected being allocated a complex transmission factor. A moderate improvement is possible as a result, but the transmission factor depends very greatly on the mask goemetry and it is therefore very difficult to generalize the method for general mask goemetries. An unsatisfactory simulation result is often produced in the case of mask geometries which deviate from the mask geometries used for determining the transmission factor.